K-Means Clustering

• K-means assumes the clusters are symmetric, there can be asymmetrical clusters.
  
• The data is assumed to be independent.
  
• Properly scaled data is important for K-Means, it can lead to uneven clusters.
  
• There is a fixed number of clusters for K-Means.
  

• Descriptive statistics/histograms/correlation matrix to visualize the spread of the data.

• Preprocess and scale data for ease of comparability.

• Libraries used: tidyverse, cluster, and factoextra. 

• The Euclidean distances are calculated to get the clustering distances measurement

• The distance data is visualized using the fviz_dist() function in R from the factoextra package. 

\[WCSS = \sum_{i=1}^{K}\sum_{j=1}^{ni}\left \| x_{ij} - c_{i} \right \|^2\]

• K is number of clusters.
  
• n_i is number of data points in cluster i.
  
• C_i is centroid.
  
• X_ij is the j^th data point in cluster I.
  

The WCSS can be used to measure how the data within a cluster are grouped. The variables that are used from the dataset are then scaled. Then, after they are scaled the next steps are:

Euclidean distance is calculated between each attribute, and the cluster center: \[ D_{euclidean}(x, Ki) = \sqrt{\sum_{i=1}^{n}((x_{i}) -(k)_{ij})^{2}} \]

Where:

• x is data point.
  
• k_i is cluster center.
  
• n is number of attributes.
  
• x_i is the i^th attribute of the data point.
  
• K_ij is the j^th attribute of the centroid of cluster i.
  

include snippets of data cleaning code. use stuff from discord

• Covariance is a statistical measure revealing the relationship between variables.
• Positive numbers indicate a positive relationship, such as the positive number at loudness and energy, telling us that as the loudness increases in a track so does the energy.
• In the other direction, the higher the negative number the smaller correlation that is involved, such as the difference between loudness and acousticness.

In the correlation plot, the darker the blue the greater the correlation between the variables. The chart shows a positive correlation between energy and loudness and a negative correlation between acousticness and energy.

• Histogram of variables to assess distribution and normality

• The point at which the line starts to curve is where we get our “k” clusters. Hence the name “Elbow Curve”
• The visual will shown a bend “elbow” due to the increasing value of K decreasing the number of datapoints. This bend is the indicator of the ideal number of clusters for our model.
• In our plot, we see that 3 is the ideal number of clusters, meaning there are 3 centroids to determine where the data points will fit the closest too.

• Three distinct clusters are shown here.

• In cluster 1, there are 2,292 records.

• In cluster 2, there are 1,263 records.

• In cluster 3, there are 3,010 records.

Centroid Center Positions:

• The ratio of between-cluster sum of squares (BSS) to total sum of squares (TSS).

• This measurement shows how well spread the clusters are between a value of 0 and 1.

• The closer to 1, the more distinct the clusters are within the dataset.

• In our model, the BSS/TSS ratio is 0.2042409, which is a pretty low ratio for this type of model. However, we determine a low number of clusters was sufficient in this model, which would also result in a low BSS/TSS ratio.

BSS/TSS Ratio: 0.2039852

• This table shows which cluster has the miminum and maximum of each attribute.
• This table briefly summarizes the types of songs we have in each cluster.

We would like to see the number of popular songs in each cluster. Just like our previous analysis we take our spotify review set and see the number of popular tracks in each cluster based on our popularity score of >57. - In cluster 1, there are 492 popular tracks. - In cluster 2, there are 405 popular tracks. - In cluster 3, there are 1,241 popular tracks.

The graph compares the groups as we use this new only_pop data to see what type of popular tracks are in each cluster.

In our k means clustering model, cluster 1 has the highest duration_min, energy, instrumentalness, liveness, loudness, and tempo. These are fast and upbeat songs that include Blinding Lights, Crazy Train, and Sweet Child of Mine. The majority of genres are pop, rock, and EDM, which make up our most popular groups. These sounds are low on acousticness, dancebilitity, speechiness, and valence. This cluster also has the lowest number of popular tracks.

In our k means clustering model cluster 2 has the highest danceability, speechiness, valence, and the highest number of popular songs for our clusters. These are cheerful and vocal songs that include Memories, Falling, and everything I wanted as its top songs. The majority of genres are pop, latin, and rock. These sounds are low on duration_min, dancebilitity and instrumentalness.

Cluster 3

In our k means clustering model cluster 3 has the highest acousticness. These are soft rock or acoustic songs that include Roxanne, The Box, and Circles. These sounds are low on energy, liveness, loudness, and tempo. This cluster is very close to having the lowest number of popular track, and the top genres are latin, rap, and pop.